Writing Algebraic Expressions

Before we can write in code, we need to know the parts of our language. An algebraic expression is a mathematical phrase that contains numbers, operations, and letters. A variable is a letter (like $x$ or $n$) that represents a number we don't know yet. A coefficient is the number that is multiplied by the variable—it's like the variable's 'partner.' Finally, a constant is a number that stands alone because its value never changes. In the expression $4x + 7$, the $4$ is the coefficient, $x$ is the variable, and $7$ is the constant.

To write expressions, you must act like a translator. Certain words tell you exactly which operation to use. Sum or increased by means addition ($+$). Difference or less than means subtraction ($-$). Product or times means multiplication ($imes$), and quotient means division ($\div$). Be careful with 'less than'! The phrase '5 less than $x$' means you start with $x$ and take 5 away, written as $x - 5$. The order is swapped!

Once you have your expression, you can 'evaluate' it. This is just a fancy word for finding the total value when you are told what the variable represents. We use substitution, which means we temporarily replace the letter with a specific number. If you have the expression $2x + 3$ and you are told $x = 5$, you simply plug the 5 into the $x$ spot. Remember to follow the Order of Operations (PEMDAS) to get the right answer!